Alessandro Oneto:Power ideals, from Fröberg conjecture to fat points

Power ideals, i.e. ideals generated by powers of linear forms, are a very fruitful field of research, especially for their connection with many other branches of commutative algebra, algebraic geometry and combinatorics. In particular, they represent the link between the Fröberg conjecture about Hilbert series of generic ideals and the study of schemes of fat points in P^n.

After an introduction about those different topics and their connections, we will focus on the study of the Hilbert series of particular classes of power ideals and fat points. These are joint works with J. Backelin and R. Fröberg.